Its core principle is that the net for catching illegal immigrants living in the UK has too many gaps, so the Home Secretary is going to add more strings to it. Immigration status checks will be able to be carried out when people apply for driving licences and bank accounts, when they rent property or when they use the NHS.

It will be a surprise to many that it is currently possible to get a driving licence, for example, while living here illegally, but it’s just an illustration of how incoherent and disconnected the approach to illegal immigration has been so far.

Two main criticisms of May’s proposals have been raised.

The first, floated by Labour and UKIP, is to say that the Government should just fix controls at the border instead. It’s obvious that effective border controls ought to be the main line of defence against illegal immigration, and as we found out yesterday the costly e-Borders system is yet to be fully operational. That must be improved. But to suggest that is all that is needed, or that this is an either/or choice, is a nonsense.

Plenty of illegal immigrants enter the country as tourists or students but overstay their visas and drop off the grid – May’s new rules will help to catch more of them, while tighter borders would do nothing to stop them arriving legitimately. It’s also the case that decades of chaotic border systems and agencies have allowed large numbers of people to live in the UK illegally; tightening the border might prevent their numbers growing but those already here will be untroubled by the law unless action is taken to identify them.

The second criticism is that the proposals turn NHS and DVLA staff, as well as landlords, into immigration officials. Sure, they’ll have new responsibilities, but is it unreasonable to ask them to make these checks? Employees of the public sector delivering public services should at least try to make sure the people they are spending taxpayers’ money on are legally entitled to it. That’s part of providing a service efficiently – when the NHS offers costly treatment to a non-resident who doesn’t pay for it, that comes at a cost to UK residents who have full legal rights and have often spent their lives paying tax.

The same goes for DVLA staff – giving a driving licence to someone here illegally helps them to continue with their crime, particularly if they are using the vehicle to work illegally. One arm of the state facilitating illegal immigration while another tries to prevent it makes the law look like an ass.

Private sector landlords have a more reasonable concern: that these new rules are an additional red tape burden on their businesses at a time when politicians already complain about the price of housing. I’ve never used the system for checking someone’s immigration status, so I can’t say how onerous it is at present, but it is only fair that these new responsibilities are matched with a helpful, swift system for carrying checks out. If new regulation is to be introduced it ought to be as affordable to obey as possible.

The basic principle still stands, though – illegal immigration is a crime, and renting houses to people who commit it is profiting from that crime. It is little different to employing illegal workers – we ask employers to ensure their staff have the right to work in the UK, why should landlords not ensure their tenants have the right to live here?

As Lord Ashcroft noted last month, the challenge with winning the debate on immigration is as much one of confidence as it is one of practicality. Having effective policies isn’t enough if no-one believes the statistics, and polling in today’s Independent suggests most people think current rules aren’t being enforced. I suspect that winning public confidence on this will be a geological process, in that it will take both time and sustained pressure.